I've lived my whole life in Texas and never assigned cardinal directions to out or over. Up and down, sure, but that seems fairly universal. No one in checking with, regardless of Texas hometown or age had any idea this was a thing, either, and that's hitting people up to 60 years old and from Austin, Houston, Dallas, and San Antonio. Maybe it's a rural Texas thing?
I went down (south) to Lubbock for College and over to Fort Worth (east) when I graduated. I still head over (west) to Lubbock occasionally because I have a sister going to Texas Tech. I go up (north) to Amarillo to visit my parents.
Maybe it's just me, but I haven't really noticed anyone using "out" to describe a direction. People do head "out" and go "out" all the time though.